examples of aliquot sequences

A prime numberp>1 has an aliquot sequences that is almost as short, namely: p, 1, 0. For example, 47, 1, 0.

Technically, all aliquot sequences are infinite, but some cease to be interesting sooner than others. Throughout this article, length will refer to the length of the aliquot sequence from its first element up to the first instance of the fixed point.

In exploring aliquot sequences with a computer, one needs to be careful not just with aliquot sequences of unknown length, but also with those where even the human operator already knows how short the sequence is. Even a sophisticated computer algebra system like Mathematica can get stuck on the aliquot sequence for 220 or 284 (amicable numbers) if the operator neglects to program in the ability to recognize cycles.